
Use Maple to perform the following tasks.
\be
	\item Factor the expression $x^3+x^2-17x+15$.
	\item Calculate the first and second derivative functions of $\ds f(x)=x^2\ln(x)$. Determine all critical points and
points of inflection of $f$, and then graph $f$, along with its first and second derivative functions, on a single set of
axes and in different colors.
    \item Graph the relation $x=\sin(y)$ on a viewing window where $\ds -\pi \leq y \leq \pi$.

    \item Graph the function $\ds f(x_1,x_2)=x_1x_2e^{1-x_1^2-x_2^2}$ in blue on a normal set of axes using
    the \mf{patch} style.

    \item Compute all products of the form $\ds i^2+j^3$, where $1 \leq i \leq 4$ and $ 1 \leq j \leq 3$.

    \item Compute the transpose, determinant, reduced row echelon form, and inverse of the matrix
    $\ds A=\begin{bmatrix} 1 & 1 & 2 \\ 2 & 4 & -3 \\ 3 & 6 &-5 \end{bmatrix}$.

    \item Compute the solution, $\vecx$, of the system of equations, $A\vecx=\vecb$, where $A$ is the matrix
    from the preceding question and where $\ds \vecb=\begin{bmatrix} 9 \\ 1 \\ 0 \end{bmatrix}$.
    \item The quantities $AB$, $B^{-1}A$, and $A+2B+D$, where $A$ is the matrix from (6),
     $\ds B=\begin{bmatrix} 4 & 0 & 3 \\ 0 & 1 & -1 \\ 2 & 2 & 0 \end{bmatrix}$, and $D$ is a 3 by 3 diagonal matrix having nonzero entries equal to 4.
    \item Graph the function $f(x)=2^x$, where $-1 \leq x \leq 5$.
    \item Graph the points, $\ds \left(i,2^i \right)$, where $i$ assumes all integer values between -1 and 5, inclusive.
    \item Create an illustration that depicts a superposition of the previous two plots.
\ee 